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9. The graph shown below is a translation of the graph of the quadratic parent function. Write the function for the graph in vertex form.

Ask by Luna Pierce. in the United States
Mar 14,2025

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To write the quadratic function in vertex form, identify the vertex \( (h, k) \) and the value of \( a \). The vertex form is \( f(x) = a(x - h)^2 + k \). Use another point on the graph to find \( a \). For example, if the vertex is at \( (2, 3) \) and another point is \( (3, 5) \), then: 1. \( h = 2 \), \( k = 3 \) 2. Substitute into the vertex form: \[ 5 = a(3 - 2)^2 + 3 \Rightarrow 5 = a(1) + 3 \Rightarrow a = 2 \] 3. The function is: \[ f(x) = 2(x - 2)^2 + 3 \] If you provide the vertex and another point, I can help you write the specific function.

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Bonus Knowledge

To convert the graph of the quadratic function into vertex form, you need to identify the vertex of the parabola, which is typically represented as \((h, k)\) in the vertex form \(f(x) = a(x-h)^2 + k\). Let’s say the vertex you identified is \((h, k)\), and you have determined the vertical stretch/compression factor \(a\) based on how the parabola opens. Plug these values into the formula: \(f(x) = a(x-h)^2 + k\). Once in this form, you can easily graph it or perform further transformations. The vertex form highlights the vertex directly, making it easier to understand the key features of the parabola and to sketch it accurately.

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